HEADS I WIN, TAILS YOU LOSE

Article published on July 28, 2011
Article published on July 28, 2011
Mike Bozoudis, aeronautical engineer Every one gambles once in a while, more or less often. Joker, lotto, lottery tickets, casino games… And whenever it comes to a win, we feel so blessed that the Goddess of Fate popped a smile at us!
So blessed and happy, that we forget all those times we were losing money…

But eventually, there comes a moment when we realize that in long term the pot is earning and we are losing money. Is the pot “luckier” than we are? Is the dice modified and the cards marked? Are the balls remotely controlled, jumping in an air flow that determines their movements? Are we simply hoodoos and jinxes? Or is it that “we are facing asymmetrical threats from outer space”? Sooner or later, we either find the answer ourselves or may the truth be revealed by John Taramas, during some New Year’s Eve TV show…

The pot is earning money, not because it is “luckier” than we are, but because

it knows exactly how much our “luck” costs. The statistics laws are camouflaged behind blinking lights, decks of colorful cards, spinning balls with numbers, and are served with dreams for a luxurious lifestyle beyond our imagination. And by this way, the pot manages to buy our “luck” at a lower price than it actually costs. In other words, the pot buys our probability to win the game at a bargain price.

What is “probability”? And how can we evaluate it?

One of the definitions for probability is that it expresses the relative frequency for an event. The relative frequency can be determined if, during the repeated trials of a random (or non deterministic) experiment, we count how many times a specific event occurred and divide by the total number of the experiment’s trials. The more the number of trials increases, the more the relative frequency tends to attain a certain value. In statistics, this phenomenon is called “the law of statistical regularity” or “normality”.

So, if we flip a coin twice and the result is “tails” both of the times, we shouldn’t just base our expectations on this result, assuming that the odds for “tails” vs. “heads” will be 100%-0% whenever we flip a coin… We should repeat this experiment many, many times before reaching any conclusion. Then we could confirm that the relative frequency of “heads” and “tails” tends to move closely around 50%. On the other hand, knowing that the odds for “heads” vs. “tails” is 50%-50%, this doesn’t mean that flipping a coin twice will necessarily result in one “heads” and one “tails”.

In such simple cases, we don’t have to repeat the experiment since we perceive the expected outcome as “common sense” or by intuition. But as for gambling, the cases are usually much more complicated...

The minimum rate of return on a bet should be our winning probability inversed. So, if our winning probability is 25%, we should require a minimum rate of return that equals to 1/0,25 = 4. Let’s see the following example:

Assume that we bet on “heads” when flipping a coin once. The probability of success is ½ so the minimum rate of return must be, at least, this probability inversed, that is 2. The probability of earning money will be on our favor if we take part in this game many times with a rate of return higher than 2.

Notice the key-phrase: “probability of earning money” and not “probability of winning the game”. The latter will always depend on statistics; the former depends on our ability to bet with a favorable rate of return!

For the Greek lotto, the “probability of winning the game” (that is to choose 6 out of 49 numbers and get all of the 6) is 1/13.983.816. But if we bet many times on this game, is the “probability of earning money” favorable for us? Of course not…The bet for choosing 6 numbers is 0,15 cents so we should demand a minimum rate of return 13.893.816 on these 0,15 cents. That is, in case of success, 2.097.572,40 € (after taxes). Does anyone remember an amount of this magnitude ever awarded to a lotto winner in Greece? Well, it is not in my intentions to disparage OPAP (the Greek Football Games Forecasting Organization). On the contrary, I recommend investing in OPAP’s shares instead of being OPAP’s customers. This way, the probability of earning money will be much higher!

Finally, a quiz for those who like challenges: “If you throw a pair of dice 50 times, I bet 5 to 1 that you won’t get more than 3 pairs of sixes”. Would you bet at a rate of return 5 to 1? Would you seek for an advice in your horoscope or in your calculator?